Sensors of all types are increasingly important aspects of life in both the military and civilian worlds. Antennas, either singularly or in arrays, comprise one type of sensor. Radio-frequency transmissions received by these antenna arrays can be of significant importance, and in many cases it can be crucial to determine the direction from which the transmissions originate. The military, particularly the Navy, needs cost-effective precision radio-frequency emitter direction-finding systems for applications including enhanced situational awareness, radar system cueing, radar to electronic sensors tracking correlation. Such capability also can be important in the civilian realm, where it can be useful in locating the direction from which received radio-frequency transmissions originate can aid in determining location information for cell phone calls to 911 emergency numbers, determining gunshot locations, or resolving ambiguities for commercial sonar arrays.
In general, direction-finding (DF) techniques can be classified as either amplitude comparison or phase comparison technologies. Amplitude comparison DF technologies are moderately priced, but provide only relatively low DF accuracy. Phase comparison technologies can provide better DF accuracy, but involve certain ambiguities that can make them prohibitively expensive.
For example, one phase comparison technique uses a linear interferometer comprising two or more antenna elements at a distance d apart. Using such an array to determine an angle of arrival (AoA) of a received radio-frequency wave involves measuring a difference between a phase of the wave received at one element and a phase of the wave received at another element. However, such phase comparison techniques also involve ambiguities in determining a direction of an incoming signal because more than one incoming angle can often result in the same measured phase difference.
Interferometer DF accuracy is a function of aperture size, with a larger array providing better performance. A conventional high-performance linear interferometer array typically has four to six antenna channels and provides a field of view of greater than 90 degrees, and so in order to provide a full 360-degree field of view, four such arrays would be needed. However, as the array gets larger, additional phase ambiguities are introduced. In order to control the ambiguity, more antenna/receiver channels are typically added, but such additional channels can make the array too large, heavy, and costly to be a fully viable system, particularly for use on board a ship or in the growing unmanned aerial vehicle (UAV) field.
To address this problem, alternate interferometer designs are being sought. The history of antenna array geometry design has been formulated as an optimization problem, for example, a problem involving relatively prime integer optimization. Radio astronomers looking for an optimal design have used interferometry principles and have studied array redundancy. See e.g., “Hoctor, R. T. et al., “Array Redundancy for Active Line Arrays,” IEEE Transactions on Image Processing, Vol. 5, No. 7, pp. 1179-1183 (July 1996). More recently, sensitivity analysis of the array manifold and its differential geometry have been explored for use as criteria for array geometry evaluation. See Manikas, A. et al., “Manifold Studies of Nonlinear Antenna Array Geometries,” IEEE Transactions on Signal Processing, Vol. 49, No. 2, pp. 497-506 (March 2001).
Sparse linear interferometers comprise one alternative interferometer design. Sparse linear interferometers are based on non-periodic antenna element placement and are set to provide maximum phase ambiguity resolution with a minimum number of channels. Due to the nature of the design of a sparse interferometer, although doubling the DF accuracy requires a doubling of the length of the array, it does not require a doubling of the number of channels, and therefore sparse linear interferometers scale very efficiently. See, e.g., Austeng, A. et al., “1D and 2D Algorithmically Optimized Sparse Arrays,” 1997 IEEE Ultrasonics Symposium 1683-1686.
These and other efforts at antenna array design are described in U.S. Pat. No. 7,330,840, “Method and Apparatus for Genetic Fuzzy Design,” issued to Sverre Nils Straatveit, one of the inventors of the present invention, the entire disclosure of which is hereby incorporated by reference herein. Other antenna array design considerations and approaches to addressing those considerations are described in the U.S. patent application entitled “Histogram for Ambiguity Visualization and Evaluation (HAVE),” Navy Case No. 98857-US 1, by Sverre Nils Straatveit and Peter W. Schuck, which was filed concurrently with the present application and the entire disclosure of which is incorporated herein by reference.